Review Slides for Final Exam

CE 374K HydrologySpring 2013

How is new knowledge discovered?

Deduction from existing knowledge

Experiment in a laboratory

Observation of the natural environment

Deduction – Isaac NewtonGiven a set of axioms and a reasoning process, derive new principles

“The ancients divided mechanics into two parts; the rational, which proceeds accurately by demonstration; and the practical.

It occurs that mechanics is so distinguished from geometry, that what is perfectly accurate is called geometrical, what is less so, is called mechanical. Yet the errors do not come from the art but from those who practice the art. In this sense rational mechanics will be the science of motions resulting from any forces whatsoever, and of the forces required to produce any motions, accurately proposed and demonstrated.” 

Isaac NewtonTrinity College, Cambridge

8 May, 1686

Experiment – Henry DarcyReplicate nature in a laboratory and identify its functional processes

“Note D is on water filtration. It includes a description of a new device that seems to simply and economically resolve the problem of filtering water to supply a large city. To obtain this result, I take into consideration the law of water flow through sand, a law that I have demonstrated experimentally.

It appears that for an identical sand, it can be assumed that the volume discharged is proportional to the head and inversely proportional to the thickness of the sand layer that the water passes through.”

Published in Paris for Imperial Corps of Bridges, Roads and Mines,1856

Observation – Charles DarwinIdentification of patterns in nature by direct observation

“When on board H.M.S. Beagle, as naturalist, I was much struck with certain facts in the distribution of the inhabitants of South America, and in the geological relations of the present to the past inhabitants of that continent. These facts seemed to me to throw some light on the origin of species -- that mystery of mysteries, as it has been called by one of our greatest philosophers. On my return home, it occurred to me, in 1837, that something might perhaps be made out on this question by patiently accumulating and reflecting on all sorts of facts which could possibly have any bearing on it.

I can here give only the general conclusions at which I have arrived, with a few facts in illustration, but which, I hope, in most cases will suffice.”

Published 24 November,1859Most accessible book of great

scientific imagination ever written

“Thus, if we denote the thickness of the sand layer by e, its surface area by s, atmospheric pressure by P, and the height of the water on the sand layer by h, we will have P+h for the pressure to which the upper end will be subjected. In addition, if P ± h0 is the pressure to which the lower surface is subjected, k is a coefficient that depends on the permeability of the layer and q is the volume discharge, we have

which reduces to

when h0 = 0 or pressure under the filter is equal to atmospheric pressure.”

Darcy’s Law

es

P+h

P ± h0

q

k

Pressurized water supply in a hospital

Description of experiments and equation, p. 455-459,as part of Appendix D in the book of 506 pages.

Sand column is 2.3 m high

0.35m diameter

Diagram from Plate 24

Hydraulic Conductivity in Test 1, 29 Oct 1855Darcy’s Law:

= = 0.09621m2

For Test 1, Q/Dh = 2.8357, L

These are reasonable numbers for “slow sand” filtersModern “rapid sand” filters have conductivities of 5-12 m/hr

The Green-Ampt conductivity for sand is 12 cm/hr

Green-Ampt Conductivity and Suction Head

0 5 10 15 20 25 30 350.01

0.10

1.00

10.00

100.00

Suction Head, ψ (cm)

Conductivity, K (cm/hr) Sand

Clay

Silt Loam

Silty Clay Loam

Loamy Sand

Sandy Clay

Sandy Loam

Loam Sandy Clay LoamClay Loam

Silty Clay

Green-Ampt Assumptions

Wetted Zone

Wetting Front

Ground Surface

Dry Soil

L

ni

z

= increase in moisture content as wetting front passes

= Suction head at “sharp” wetting front

Conductivity, K

L = Wetted depth

K = Conductivity in wetted zone

Ponded Water 0h

0h = Depth of water ponding on surface (small)

Green – Ampt Infiltration (Cont.)

• Apply finite difference to the derivative, between – Ground surface– Wetting front

Kz

Kf

Wetted Zone

Wetting Front

Ground Surface

Dry Soil

L

i

z0,0 z

,Lz

KL

KKz

KKz

Kf

0

0

F

L

LtF )(

1

FKf

Kz

Kf

Green – Ampt Infiltration

Wetted Zone

Wetting Front

Ponded Water

Ground Surface

Dry Soil

0h

L

n

i

z

LLtF i )()(

dt

dL

dt

dFf

zh

Kz

Kf

fz

hKqz

MoistureSoilInitial

Front WettingtoDepth

i

L

Drought in Texas – US Drought Monitor

April 2013September 2011

Texas 98% in drought12% in D4

Texas 99% in drought87% in D4

http://droughtmonitor.unl.edu/

In 2011, Texas and Oklahoma had the hottest summer ever recorded in the history of the United States

Trends in Drought Severity in Texas

2006 2009 2011200420022000

Drought and GRACE

Perc

ent o

f Are

a in

Dro

ught

September 2011

GRACE

US Drought Monitor

At peak drought, Texas had a 100 Km3 water deficit(equivalent to 70 Lake Travis’s)

US Drought Monitor is closely correlated with the GRACE data

Dam 7

805 ft

829 ft836 ft

HEC-HMS representation

Elevation-Storage Curve, Dam 7

Emergency Spillway, 829

Top of Dam, 836

Storage-Discharge Curve, Dam 7

Emergency Spillway, 829

Top of Dam, 836

Watershed W1820

Reach R580

Steady Flow Solution

Right Overbank Left Overbank

Channel centerlineand banklines

Cross-section

One-Dimensional Flow Computations

Floodplain Delineation

National Flood Insurance Program

• Begun in 1968• Federal government provides a national flood insurance

program• Local communities regulate land development in floodplains• Requires floodplain maps

– Base Flood Elevation for 100 year flood is the key– Keep building floor elevations above this level– Keep building out of 100 year inundated area

Map Showing Inundation in Bexar County, Texas

Base Elevation Data in Detail—Light Detection and Ranging (lidar)

• Lidar uses single laser pulses to see through or between the trees to create thousands of 3-D point measurements per second

• Advantage: The most accurate method for mapping the bare-earth terrain in vegetated areas

• Disadvantage: Poor for generation of breaklines for edges such as shorelines, tops & bottoms of stream banks,

Base Elevation Data in Detail—Strengths and Weaknesses Compared

Digital elevation model from National Elevation Dataset Photogrammetry/digital orthophoto

Digital elevation model from lidar Digital elevation model from IFSAR

1. Existing elevation data are old, and there is a large gap between their accuracy and the accuracy required for floodplain mapping

2. The required elevation mapping technology exists and has been commercially deployed such that implementing Elevation for the Nation is technically feasible with lidar.

Why is Elevation for the Nation Needed?

http://www.nap.edu/catalog.php?record_id=11829

Can Download the report the report in pdf format at National Academy Press